Question

The line joining $(5,0)$ to $((10 \cos \theta, 10 \sin \theta)$ is divided internally in the ratio $2: 3$ at $P$. If $q$ varies, then the locus of $P$ is

• A. a pair of straight lines
• B. a circle
• C. a straight line
• D. None of these

Answer 1

Answer: (B)

a circle

Answer 2

Let $P(x, y)$ be the point dividing the join of $A$ and $B$ in the ratio $2: 3$ internally, then $x=\frac{20 \cos \theta+15}{5}=4 \cos \theta+3$ $\Rightarrow \cos \theta=\frac{x-3}{4} \ldots$..(i) $y=\frac{20 \sin \theta+0}{5}=4 \sin \theta$ $\Rightarrow \sin \theta=\frac{y}{4} \ldots$ (ii) Squaring and adding (i) and (ii), we get the required locus $(x-3)^{2}+y^{2}=16$, which is a circle.